According to the JavaDoc, jEditorPane is capable of supporting HTML 3.2 and CSS1, which are considered as the latest standards at that time. However, it is not recommended to use it for rendering modern web pages.
But you can still try the following workaround:
import javax.swing.text.html.HTMLEditorKit;
import javax.swing.text.html.StyleSheet;
HTMLEditorKit kit = new HTMLEditorKit();
jEditorPane.setEditorKit(kit);
URL url = new URL(location of your stylesheet);
StyleSheet styleSheet = new StyleSheet();
styleSheet.importStyleSheet(url)
kit.setStyleSheet(styleSheet);